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Unformatted text preview: ectance. Variations in lighting can be included directly in the mixing model by defining a “shade” endmember that can mix with the actual material spectra. A shade spectrum can be obtained directly from a deeply shadowed portion of the image. In the absence of deep shadows, the spectrum of a dark asphalt surface or a deep water body can approximate the shade spectrum, as in the example to the right. Portion of an AVIRIS scene with forest, bare and vegetated fields, and a river, shown with a color-infrared band combination (vegetation is red). Fraction images from linear unmixing are shown below. Vegetation fraction Water / shade fraction Soil fraction page 19 Introduction to Hyperspectral Imaging Defining Image Endmembers
When spectral endmembers are defined from a hyperspectral image, each image endmember should have the maximum abundance of the physical material that it represents. (Ideally, each endmember would be a single pure material, but “pure” pixels of each endmember may not be present in the image). If image spectra are represented as points in an n-dimensional scatterplot, the endmembers should correspond to cusps at the edge of the cloud of spectral points. One common procedure for isolating candidate image endmembers involves several steps. Because of the high degree of correlation between adjacent spectral bands, the dimensionality of the dataset first can be reduced by applying the Minimum Noise Fraction (MNF) transform and retaining the small number of noise-free components. The MNF transform (Green et al. 1988) is a noise-adjusted principal components transform that estimates and equalizes the amount of noise in each image band to ensure that output components are ordered by their amount of image content. Second, an automated procedure is applied to the MNF components to find the extreme spectra around the margins of the n-dimensional data cloud. One such procedure is the Pixel Purity Index (PPI). It examines a series of randomly-oriented directions radiating outward from the origin of the coordinate space. For each test direction, all spectral points are projected onto the test vector, and the extreme spectra (low and high) are noted. As directions are tested, the process tallies the number of times each image cell is found to be extreme. Pixels with high values in the resulting PPI raster should correspond primarily to the edges of the MNF data cloud. In the third step, the PPI raster is used to select pixels from the MNF dataset for viewing in a rotating n-dimensional scatterplot (using a tool such as the n-Dimensional Visualizer in the TNTmips Extreme spectra Hyperspectral Analysis process). By viewing the PPI spectral cloud from various directions, the analyst can identify significant directions, mark the spectral points that are extreme in those directions, and save an image of the marked cells. Finally, the marked cell image is overlaid MNF Component 1 on the original hyperspectral image and Simple two-component plot showing used as a guide to select and examine the one of the random vector directions image spectra. The best candidate (arrow) tested by the Pixel Purity Inendmember spectra are then saved in a dex procedure. All spectral points are projected to each test vector, and exspectral library for use in unmixing the hytreme points are noted. perspectral image.
MNF Component 2 page 20 Introduction to Hyperspectral Imaging Partial Unmixing
Some hyperspectral image applications do not require finding the fractional abundance of all endmember components in the scene. Instead the objective may be to detect the presence and abundance of a single target material. In this case a complete spectral unmixing is unnecessary. Each pixel can be treated as a potential mixture of the target spectral signature and a composite signature representing all other materials in the scene. Finding the abundance of the target component is then essentially a partial unmixing problem. Methods for detecting a target spectrum against a background of unknown spectra are often referred to as matched filters, a term borrowed from radio signal processing. Various matched filtering algorithms have been developed, including orthogonal subspace projection and constrained energy minimization (Farrand and Harsanyi, 1994). All of these approaches perform a mathematical transformation of the image spectra to accentuate the contribution of the target spectrum while minimizing the background. In a geometric sense, matched filter methods find a projection of the n-dimensional spectral space that shows the full range of abundance of the target spectrum but “hides” the variability of the background. In most instances the spectra that contribute to the background are unknown, so most matched filters use statistical methods to estimate the composite background signature from the image itself. Some methods only work well when the target material is rare and does not contribute significantly to the background signature. A modified version of matched filtering uses derivatives of the spectra rather than the spectra themselves, which improves the matching of spectra with differing ove...
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